Recently,　Gabor　analysis　on　locally　compact　abelian　(LCA)　groups　has　interested　some　mathematicians.　The　half　real　line　R+　=　(0,　infinity)　is　an　LCA　group　under　multiplication　and　the　usual　topology,　with　the　Haar　measure　d　mu　=　dxx.　This　paper　addresses　rationally　sampled　Gabor　frames　for　L2(R+,　d　mu).　Given　a　function　in　L2(R+,　d　mu),　we　introduce　a　new　Zak　transform　matrix　associated　with　it,　which　is　different　from　the　conventional　Zibulski-Zeevi　matrix.　It　allows　us　to　define　a　function　by　designing　its　Zak　transform　matrix.　Using　our　Zak　transform　matrix　method,　we　characterize　and　express　complete　Gabor　systems,　Bessel　sequences,　Gabor　frames,　Riesz　bases　and　Gabor　duals　of　an　arbitrarily　given　Gabor　frame　for　L2(R+,　d　mu),　and　prove　the　minimality　of　the　canonical　dual　frames　in　some　sense.　Some　examples　are　also　provided　to　illustrate　the　generality　of　our　theory.(c)　2023　Elsevier　Inc.　All　rights　reserved.